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Diffstat (limited to 'NaturalTransformation/Instance/EmptyMultiset.agda')
| -rw-r--r-- | NaturalTransformation/Instance/EmptyMultiset.agda | 34 |
1 files changed, 34 insertions, 0 deletions
diff --git a/NaturalTransformation/Instance/EmptyMultiset.agda b/NaturalTransformation/Instance/EmptyMultiset.agda new file mode 100644 index 0000000..bfec451 --- /dev/null +++ b/NaturalTransformation/Instance/EmptyMultiset.agda @@ -0,0 +1,34 @@ +{-# OPTIONS --without-K --safe #-} + +open import Level using (Level; _⊔_) + +module NaturalTransformation.Instance.EmptyMultiset {c ℓ : Level} where + +import Function.Construct.Constant as Const + +open import Categories.NaturalTransformation using (NaturalTransformation; ntHelper) +open import Categories.Functor using (Functor) +open import Data.Setoid.Unit {c} {c ⊔ ℓ} using (⊤ₛ) +open import Categories.Functor.Construction.Constant using (const) +open import Data.Opaque.Multiset using (Multisetₛ; []ₛ; mapₛ) +open import Functor.Instance.Multiset {c} {ℓ} using (Multiset) +open import Function.Construct.Constant using () renaming (function to Const) +open import Relation.Binary using (Setoid) +open import Data.Setoid using (_⇒ₛ_) +open import Function using (Func; _⟶ₛ_) +open import Function.Construct.Setoid using (_∙_) + +opaque + unfolding mapₛ + map-[]ₛ + : {A B : Setoid c ℓ} + → (f : A ⟶ₛ B) + → (open Setoid (⊤ₛ ⇒ₛ Multisetₛ B)) + → []ₛ ≈ mapₛ f ∙ []ₛ + map-[]ₛ {B = B} f = Setoid.refl (Multisetₛ B) + +⊤⇒[] : NaturalTransformation (const ⊤ₛ) Multiset +⊤⇒[] = ntHelper record + { η = λ X → []ₛ {Aₛ = X} + ; commute = map-[]ₛ + } |
